I'll be in Chicago for exactly one breakfast -- that's how I measure time, rather than in days or hours -- next week on a weekday, staying at the W on Lake Shore. Proximity isn't a huge deal, though I'd rather not be in a cab for 45 minutes each way.
Preliminary research says I should go to one of these three; please let me know your expert thoughts:
2) Lou Mitchell's
3) Ann Sather
Lou Mitchell's Restaurant
565 W Jackson Blvd, Chicago, IL 60661